RAID-1: Errors and Erasures calculations

RAID-1 Overheads (treating RAID-1 and RAID-10 as identical)

N = number of drives mirrored. N=2 for duplicated
G = number of drive-sets in a Volume Group.
\(N \times G\) is the total number of drives in Volume Group.
An array may be composed of many Volume Groups.

Per-Disk:

• Effective Capacity
• N=2. \( 1 \div 2 = 50\% \) [duplcated]
• N=3. \(1 \div 3 = 33.3\% \) [triplicated]

• I/O Overheads & scaling
• Capacity Scaling: linear to max disks.
• Random Read: \(N \times G \rm\ of\ rawdisk = N \times G \rm\ singledrive = RAID-0\)
• Randdom Write: \(1 \times G \rm\ of\ rawdisk = 100\% \rm\ singledrive\)
• Streaming Read: \(N \times G \rm\ of\ rawdisk = N \times G \rm\ singledrive = RAID-0\)
• Streaming Write: \(1 \times G \rm\ of\ rawdisk = 100\% \rm\ singledrive\)

mathjax test & Demo

MathJax setup in Blogger:
http://mytechmemo.blogspot.com.au/2012/02/how-to-write-math-formulas-in-blogger.html

MathJax Examples

Note:

1. I had to hunt for the "HTML/Javascript" gadget, down the list aways.
2. I ended up putting the gadget in as a footer.
3. You'll have to add that gadget to all blogs you want it to work for.
4. Preview and Edit mode don't compute the TeX. You need to save the doc, then view the post.
5. In compose "Options", "Line Breaks", I'm using 'Press "Enter" for line breaks.
6. The "MyTechMemo" author doesn't use the exact code he suggests, though it works for me. His actual gadget is:

Powered by <a href="http://www.mathjax.org/docs/1.1/start.html">MathJax</a>

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>


Alternate Hub Config in gadget, replace just first line.

MathJax.Hub.Config({
        TeX: { equationNumbers: { autoNumber: "AMS" } },
         tex2jax: {
                    inlineMath: [ ['$','$'], ["\\(","\\)"] ],
                   displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
                   processEscapes: true }
   });

Using "all", numbers all equations.
"AMS" numbers only specified equations.

<script type="text/x-mathjax-config">
MathJax.Hub.Config({
TeX: { equationNumbers: {autoNumber: "all"} }
});
</script>


RAID++: Erasures aren't Errors

A previous piece in this series starts as quoted below the fold, raising the question: The Berkeley group in 1987 were very smart, and Leventhal in 2009 no less smart, so how did they both make the same fundamental attribution error? This isn't just a statistical "Type I" or "Type II" error, it's conflating and confusing completely differences sources of data loss.

RAID, Archives and Tape v Disk

There's a long raging question in I.T. Operations: How best to achieve data? [What media to use?]
This question arose again for me as I was browsing retail site.

Conclusions:

1. The break-even for 2.5TB/6.25TB tapes is 85 and 140 tapes (compressed/uncompressed), or
• $13,150 and $17,400 capital investment.
2. At just 2 times data duplication, uncompressed tapes are not cost effective.
• Enterprise backup show data duplication rates of 20-50 times.
3. Compressed tapes are cost-effective up to 5-times data duplication.
• If you run 10 Virtual Machines and do full backups, you've passed that threshold.

Retail Disk prices, Enterprise drives, grouped by manufacturer & type

Table of current retail prices for various types of disk with cost-per-GB.
Only Internal drives, Hard Disks.

Disclaimer: This table is for my own point-in-time reference, does not carry any implicit or explicit recommendations or endorsement for the retailer, vendor or technologies.

Most drives are from a single manufacturer, Western Digital, to allow like-for-like comparisons.
Most manufacturers are close to the same pricing for the same specs.

• There is ~$25 extra for SAS interface over SATA [1TB WD 'RE', SAS vs SATA]
• There's ~$30/TB extra for higher spec drives [2TB & 3TB, WD SATA, NAS vs RE]
• WD sell four 3.5" 1TB drives [03, 04, 26, 41]
• SAS vs SATA, ~$25
• about double for 10,000RPM over 7,200RPM (Velociraptor vs RE)
• about 25% less for the Intellipower, 'Capacity' drive
• While it's cheaper with Seagate to go from 15,000RPM/3.5" to 10,000RPM/2.5", there's no simple relation for the discount.

Western Digital list these "Purchase Decision Criteria" for drives:

• Capacity [GB]
• Workload Capability [duty cycle or TB read/write per year]
• Reliability [MTBF and BER]
• Cost/GB
• Performance [sustained throughput,  latency or IO/sec = {RPM, seek time}]
• Power used [not included by WD]
• Racking density [not included by WD]

Historical External Disk Storage Data: IDC Worldwide tracking report

Data from IDC's Quarterly Worldwide External Disk Storage Systems Factory Revenues series (Press Releases). Multiply quarterly values by 4 for an approx yearly value. Full data not available prior to 2011.
For 2013: US$24.4 billion and 34.6PB.